CN112861418A - Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network - Google Patents

Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network Download PDF

Info

Publication number
CN112861418A
CN112861418A CN202011568052.0A CN202011568052A CN112861418A CN 112861418 A CN112861418 A CN 112861418A CN 202011568052 A CN202011568052 A CN 202011568052A CN 112861418 A CN112861418 A CN 112861418A
Authority
CN
China
Prior art keywords
value
data
grnn
icing
global
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202011568052.0A
Other languages
Chinese (zh)
Inventor
汪峰
毛锦伟
李鹏
周华华
方世书
谭小平
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
China Three Gorges University CTGU
Original Assignee
China Three Gorges University CTGU
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by China Three Gorges University CTGU filed Critical China Three Gorges University CTGU
Priority to CN202011568052.0A priority Critical patent/CN112861418A/en
Publication of CN112861418A publication Critical patent/CN112861418A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • Computer Hardware Design (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

A method for predicting the short-term icing thickness of a stay cable based on a GA-WOA-GRNN network comprises the following steps: the method comprises the following steps: according to the growth rule of the icing of the stay cable, selecting the influence factors with larger cable icing relevance, and determining a training set and a test set of sample data; step two: carrying out data normalization processing on the sample data; step three: dividing the normalized data into a plurality of groups by using a cross validation method, wherein each group of data is used as an input sample of a GRNN prediction model, and a corresponding icing thickness value is used as an output value of the model to construct a GRNN model training sample matrix; step four: optimizing a smoothing factor sigma of a GRNN (generalized regression neural network) algorithm by using a GA-WOA (genetic algorithm-word on array) optimization algorithm, and taking the mean square error of an output value and an actual value of a training sample as a fitness function so as to obtain a minimum error prediction model; and predicting the short-term icing thickness of the stay cable through the steps.

Description

Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network
Technical Field
The invention relates to the field of disaster prevention and reduction and safety early warning of bridge structures, in particular to prediction of icing thickness of a stay cable of a cable-stayed bridge.
Background
The bridge has the advantages of large spanning capacity along with the cable-stayed bridge, light structure and beautiful shape, and is an important bridge type of a large-span bridge. Under the action of wet and cold air temperature in winter, the icing phenomenon is easy to occur on the surface of the winter stay cable, and disasters in different modes are induced. The shape of the cross section of the stay cable can be changed by ice coating to form an unstable pneumatic appearance, so that a large-amplitude galloping phenomenon is generated, a PE pipe outside the stay cable is cracked due to the vibration, the stay cable and an anchoring system are corroded and damaged, and the service performance and safety of a bridge structure are influenced. Secondly, when the ice coating is subjected to temperature change or structural vibration, the phenomenon of falling of ice can occur, and the safety of vehicles and pedestrians on the bridge deck is seriously threatened.
At present, for forecasting the ice coating of the stay cable in the middle and long term in winter, the early design and planning stage of the stay cable is mainly focused, meteorological data of an ice-prone area in winter for 1-3 months are generally selected, and an ice coating extreme value which can be reached in the future is obtained through analysis of the middle and long term climatic conditions, so that the ice disaster resistance of the stay cable is improved; however, the ice coating growth process has the characteristics of non-static and non-time sequence, so that the prediction result has larger error in the application of medium and long-term data modeling calculation, the reliability of the ice resistance of the stay cable is reduced, and the ice coating growth process is difficult to apply to actual bridge engineering. The method has the advantages that the influence rule of characteristic factors on the icing growth of the stay cable can be effectively excavated according to the short-term icing growth value of the stay cable in winter, the icing prediction precision in 24h in the future is improved, workers are effectively guided to arrange on duty, a deicing scheme is formulated, the disaster prevention and reduction operation efficiency is improved, and unnecessary economic loss is reduced. However, compared with medium-and long-term icing, short-term icing lacks a large amount of sample data, the error between the calculation result of a statistical analysis model and an actual value is large, the current method for predicting the short-term icing mainly adopts a neural network modeling mode, a BP neural network, a Generalized Regression Neural Network (GRNN) and the like are common, and the generalized regression neural network has the advantages of few adjusting parameters, low artificial interference, strong nonlinear approximation capability and the like and is widely used in a prediction model; however, the space complexity of the traditional GRNN is high in the solving process, and a large number of characteristics need to be relied on, so that the precision is not high when short-term icing is processed.
Therefore, in order to ensure the safe operation of the cable-stayed bridge in the area easy to ice in winter, a short-term icing prediction model of the stay cable with high prediction precision and strong generalization capability needs to be established urgently, and decision support such as early warning and the like is provided for the anti-ice disaster reduction work of the stay cable.
Disclosure of Invention
The invention aims to establish a stay cable short-term icing prediction model with high prediction precision and strong generalization capability, and provide decision support such as early warning and the like for the anti-icing and disaster-reducing work of a stay cable, so as to solve the technical problem that the short-term icing cannot be accurately predicted by depending on a large number of samples in the existing stay cable winter icing prediction; the method can also solve the problems that the genetic algorithm is complex in structure and the whale algorithm is easy to fall into local optimum, and greatly improves the operation speed and the actual processing speed.
The purpose of the invention is realized by adopting the following technical scheme:
a method for predicting the short-term icing thickness of a stay cable based on a GA-WOA-GRNN network comprises the following steps:
the method comprises the steps of firstly, selecting influence factors with large cable icing relevance according to the growth rule of the stay cable icing, and determining a training set and a test set of sample data. Wherein, the thickness of the ice coating is taken as an output value Y, and an inclination angle, humidity, temperature, wind speed, rainfall and the like are taken as input vectors X;
step two, because the monitoring data selected in the text often have different dimensions and dimension units, the condition can influence the result of data analysis, and in order to eliminate the dimension influence among the indexes, data normalization processing is required to be carried out so as to solve the comparability among the data indexes;
dividing the normalized data into two groups of data by using a cross validation method, wherein each group of data is used as an input sample of a GRNN prediction model, and a corresponding icing thickness value is used as an output value of the model to construct a GRNN model training sample matrix;
step four, optimizing a smoothing factor sigma of a GRNN network algorithm by using a GA-WOA optimization algorithm, and taking the Mean Square Error (MSE) of the output value of a training sample and the actual value as a fitness function to obtain a minimum error prediction model in an allowed period;
and step five, continuously optimizing the smoothing factor of the GRNN by judging conditions (whether the set iteration times is reached), and inputting the influence factor data obtained by the latest actual measurement and the corresponding icing thickness data serving as test samples into an optimized model for prediction.
Predicting a test case by adopting the GA-WOA optimized GRNN model, acquiring main relevant factors influencing the icing of the stay cable, preprocessing the sample data, and then training the GRNN model as the sample data; and meanwhile, selecting data which does not participate in training as a test set, and verifying the effectiveness of the model. The final result shows that the prediction precision is improved to a certain extent, and the method can be used for short-term prediction of the stay cable ice coating in winter.
In the first step, meteorological information and stayed cable parameter information of the stayed cable are taken, near-day short-term data are usually selected, wherein the meteorological information data comprise temperature, relative humidity, precipitation, wind speed, air pressure and the like, and the stayed cable parameter information mainly comprises a cable inclination angle and a diameter;
the invention obtains the relevance of the characteristic parameters through grey relevance analysis, and the method comprises the following specific steps:
1) the comparison object (evaluation object) and the reference number series (evaluation criterion) are determined. Let m evaluation objects, n evaluation indexes, and x reference number0＝{x0(k) 1,2, …, n, the comparison column being xi＝{xi(k)|k＝ 1,2,…,n},i＝1,2,…,m。
2) And determining the weight corresponding to each index value. The weight w ═ w corresponding to each index can be determined by an analytic hierarchy process or the like1,…,wn]Wherein w isk(k is 1,2, …, n) is a weight corresponding to the k-th evaluation index.
3) Calculating a gray correlation coefficient formula:
Figure RE-GDA0002960127580000031
for comparison of the correlation coefficient of the sequence xi to the reference sequence x0 on the k-th index, where ρ ∈ [0,1]]Is the resolution factor. Wherein, it is called
Figure RE-GDA0002960127580000032
Two-stage minimum differences and two-stage maximum differences are respectively provided.
Generally, the larger the resolution coefficient ρ, the larger the resolution; the smaller ρ, the smaller the resolution.
4) The gray-weighted relevance is calculated. The grey-weighted relevance is calculated by the formula:
Figure RE-GDA0002960127580000033
in the formula: r isiGray-weighted relevance, W, of the ideal object for the ith evaluation objectiThe weight corresponding to the ith evaluation index;
5) and (5) evaluating and analyzing. And sequencing the evaluation objects according to the gray weighted association degree, and establishing the association sequence of the evaluation objects, wherein the greater the association degree is, the better the evaluation result is.
In order to improve the prediction accuracy of the algorithm model, remove some redundant features and facilitate the discovery and the mining of internal features by the GRNN model, the influence factors with small relevance need to be eliminated, and the characteristic factors with large influence on the relevance are selected.
In the first step, the thickness of the ice coated on the stay cable is taken as an output Y(n)，Y(n)＝{Y(1),Y(2),…Y(n)Is given as [ X ] with the factor sequence as the input vectorij]In this document, j groups of data are selected from 5 influencing factors (i ═ 5), and an i × j input matrix is constructed:
Figure RE-GDA0002960127580000041
in the second step, to eliminate the dimension effect of the variable, normalization (interval value is [0, 1]) is used to preprocess the data, and the basic formula is:
Figure RE-GDA0002960127580000042
wherein x isminIs the minimum value of the original data; x is the number ofmaxIs the maximum of the original data.
In the third step, dividing the normalized samples into K groups, making a verification set for each subset data respectively, using the other subset data as a training set to obtain K-fold grouping cross verification, wherein the process is as follows:
the normalized data set is randomly divided equally into K sub-data sets { S1,S2,…SkThe specific method of the invention is as follows: each subset SiAnd respectively making a verification set once, and taking the rest K-1 sub-data sets as training sets to obtain predicted values under K (K is 2) models.
Transferring the grouped training sample set (input variable) to a mode layer, wherein the neuron number of the mode layer is equal to the number j of the learning samples, and the transfer function of the mode layer is as follows:
Figure RE-GDA0002960127580000043
x in the formula is a network input variable; xiThe learning sample corresponding to the ith neuron.
Two types of neurons are used in the summation layer for summation. One of them is to sum the outputs of all the neurons in the mode layer, where the connection weight between the mode layer and each neuron is 1, and the transfer function is:
Figure RE-GDA0002960127580000044
the other type performs weighted summation on neurons of all mode layers, and the transfer function is:
Figure RE-GDA0002960127580000045
wherein the connection weight of the ith neuron in the mode layer and the jth numerator summation neuron in the summation layer is the ith output sample YiThe jth element in (a);
the number of neurons in the output layer is equal to the dimension k of the output vector in the learning sample, the output of each neuron summation layer is divided, and the output of the neuron j corresponds to the estimation result
Figure RE-GDA0002960127580000046
The jth element of (a), namely:
Figure RE-GDA0002960127580000051
in the fourth step, the Mean Square Error (MSE) of the output value of the training sample and the actual value is used as a fitness function; in the determined search space, each individual self optimal solution is searched through iteration, in each iteration, the individual can search an extreme value pbest and a global extreme value gbest, and the self position is updated mainly through a formula, wherein the updating formula is as follows:
Figure RE-GDA0002960127580000052
wherein: t is the number of iterations, XtIs the current position vector;
Figure RE-GDA0002960127580000053
the current global optimal position vector is obtained;
Figure RE-GDA0002960127580000054
to enclose the step size, coefficient vectors a and C are defined as follows:
A＝2a*rand1-a (9)
C＝2*rand2 (10)
wherein, rand1And rand2Is [0,1]]Random numbers generated uniformly within the range; a is a convergence factor, which decreases linearly from 2 to 0 with the number of iterations t, i.e.:
a＝2-2t/tmax (11)
tmaxis the maximum number of iterations.
With the reduction of the convergence factor a, the individual position can reach the optimal position between the time t and the global position at the time t +1, which means that the individual position always moves in the contraction enclosure in the optimization process, and in order to achieve the effect of the optimization mode, the individual position is searched in a spiral motion mode, and the mathematical model is as follows:
Figure RE-GDA0002960127580000055
wherein:
Figure RE-GDA0002960127580000056
as the distance between whale and the current globally optimal individual, b is a limiting constant, and l is [ -1,1 [ -1]A random number in between.
In order to solve the synchronization problem of whale individuals in hunting behaviors, the selected contraction surrounding mechanism and the spiral updating position probability are both assumed to be 0.5, and the model is as follows:
Figure RE-GDA0002960127580000057
wherein P is a random number generated uniformly distributed within [0,1 ].
When the coefficient vector | A | >1 represents that whales swim outside the contraction enclosure, the whale individuals randomly search according to the positions of the whales, and the mathematical model is as follows:
Figure RE-GDA0002960127580000061
wherein,
Figure RE-GDA0002960127580000062
is a randomly selected whale individual position vector.
Given cross probability PcFor the corresponding individual WiAnd WjIs crossed, wherein the cross formula is as follows:
Figure RE-GDA0002960127580000063
wherein the formula is as follows: alpha is alpha1And alpha2Is [0,1]]A random number in between;
given probability of variation PmAnd carrying out mutation operation on the individuals to obtain new individuals.
Figure RE-GDA0002960127580000064
f(g)＝r2(1-g/Gmax) (18)
In the formula amaxAnd aminIs represented as gene aijUpper and lower bounds of (1); r is2Is usually [0,1]]The random number of (1); g represents the current iteration number; gmaxThe maximum number of evolutions;
if p <0.5 and | A | > is more than or equal to 1, the invention uses the particle swarm optimization for reference, and the output value is subjected to self-adaptive variation updating, and the formula is as follows:
Figure RE-GDA0002960127580000065
Figure RE-GDA0002960127580000066
omega is a weight coefficient, GmaxTo the maximum number of iterations, GiFor the current number of iterations,
Figure RE-GDA0002960127580000067
for the current global optimum positionThe vector, A and C are both coefficient vectors.
And updating the local extremum and the global extremum. And comparing the current fitness value with the historical optimal fitness value, if the current fitness value is more optimal, updating the current fitness value to be a local extremum pbest, further comparing the current fitness value with the global extremum, and selecting the optimal value as the global extremum gbest.
And judging whether a termination condition is reached. The maximum iteration number is selected as a termination condition, and if the maximum iteration number is reached, the calculation is stopped. If not, jumping to step four. The fitness value is recalculated. And (5) calculating the individual fitness value after genetic manipulation.
And selecting an individual position corresponding to the minimum fitness value, namely a smoothing factor sigma, establishing a GRNN model by using the optimal smoothing factor, and predicting the test sample.
A method for obtaining fitness value of individual includes the following steps,
step 1) searching a local extreme value pbest;
step 2) searching a global extreme value gbest;
step 3), updating the local extreme value and the global extreme value;
and 4) judging whether a termination condition is reached, if so, stopping, otherwise, jumping to the step 1), and searching for the fitness value again.
And taking the mean square error of the output value and the actual value of the training sample as a fitness function, searching the self optimal solution of each individual through iteration in a determined search space, and searching a local extremum pbest and further searching a global extremum gbest in each iteration.
When searching for the local extremum pbest and the global extremum gbest, the self position is continuously updated, and the searching is performed in a spiral motion mode.
In step 3), when updating the local extremum and the global extremum, comparing the current fitness value with the historical optimal fitness value, if the current fitness value is better than the historical optimal fitness value, updating the current fitness value to the local extremum pbest, further comparing the current fitness value with the global extremum, and selecting the optimal value as the global extremum gbest.
Compared with the prior art, the method has the following technical effects:
1) the method comprehensively considers the influence of various factors on the icing of the stay cable, can accurately predict the icing thickness of the stay cable, and has strong prediction precision and generalization capability;
2) in order to solve the defects that the genetic algorithm is complex in structure, the whale algorithm is easy to fall into local optimum and the like, the crossing and mutation operators of the GA algorithm are introduced into the WOA algorithm, individual populations are updated and optimized, the WOA algorithm is prevented from falling into local optimum solution, the structure is simple, and the operation speed is greatly improved;
3) the method combines the influence factors (weather, inclination angle and the like) of icing to realize the prediction of the icing of the stay cable in a future period of time; on the basis of monitoring data, an icing forming mechanism is further combined, and a machine learning mode is adopted to train and predict a target area, so that the target area is more comprehensive and accurate;
4) compared with the traditional prediction models such as BPNN and SVM, the improved GRNN neural network is adopted, so that the interference of subjective factors on model parameters is reduced, and the training precision of the algorithm is improved;
5) by introducing the crossover and mutation operations of the genetic algorithm into the WOA and applying the mixed GA-WOA algorithm to search the optimal value of the GRNN network smoothing factor, the defect that the traditional GRNN network smoothing factor is difficult to determine is overcome, and the defects that the WOA algorithm is too slow in convergence speed and easy to fall into local optimization and the like are effectively overcome. The advantages of the WOA on the global search capability in the optimizing process are guaranteed, and meanwhile the convergence speed is improved;
6) the neural network model is established based on the monitoring data, the sample data acquisition mode is convenient and fast, the application maturity is high, the method can be effectively applied to the actual engineering icing prediction, the defects of the traditional mathematical physical model are overcome, the flexibility is good, and the universality is high.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a GRNN structure according to the present invention;
FIG. 3 is a comparison graph of the predicted effects of 4 models in the examples;
FIG. 4 is a plot of temperature information sample data as contemplated by an embodiment of the present invention;
FIG. 5 is a graph of relative humidity information sample data as contemplated by an embodiment of the present invention;
FIG. 6 is a graph of wind speed information sampling data involved in an embodiment of the present invention;
fig. 7 is a diagram of rainfall information sampling data according to an embodiment of the present invention.
Detailed Description
A method for predicting the short-term icing thickness of a stay cable based on a GA-WOA-GRNN network comprises the following steps:
the method comprises the steps of firstly, selecting influence factors with large cable icing relevance according to the growth rule of the stay cable icing, and determining a training set and a test set of sample data. Wherein, the thickness of the ice coating is taken as an output value Y, and an inclination angle, humidity, temperature, wind speed, rainfall and the like are taken as input vectors X;
step two, because the monitoring data selected in the text often have different dimensions and dimension units, the condition can influence the result of data analysis, and in order to eliminate the dimension influence among the indexes, data normalization processing is required to be carried out so as to solve the comparability among the data indexes;
dividing the normalized data into two groups of data by using a cross validation method, wherein each group of data is used as an input sample of a GRNN prediction model, and a corresponding icing thickness value is used as an output value of the model to construct a GRNN model training sample matrix;
step four, optimizing a smoothing factor sigma of a GRNN network algorithm by using a GA-WOA optimization algorithm, and taking the Mean Square Error (MSE) of the output value of a training sample and the actual value as a fitness function to obtain a minimum error prediction model in an allowed period;
and step five, continuously optimizing the smoothing factor of the GRNN by judging conditions (whether the set iteration times is reached), and inputting the influence factor data obtained by the latest actual measurement and the corresponding icing thickness data serving as test samples into an optimized model for prediction.
Predicting a test case by adopting the GA-WOA optimized GRNN model, acquiring main relevant factors influencing the icing of the stay cable, preprocessing the sample data, and then training the GRNN model as the sample data; and meanwhile, selecting data which does not participate in training as a test set, and verifying the effectiveness of the model. The final result shows that the prediction precision is improved to a certain extent, and the method can be used for short-term prediction of the stay cable ice coating in winter.
In the first step, meteorological information and stayed cable parameter information of the stayed cable are taken, near-day short-term data are usually selected, wherein the meteorological information data comprise temperature, relative humidity, precipitation, wind speed, air pressure and the like, and the stayed cable parameter information mainly comprises a cable inclination angle and a diameter;
the invention obtains the relevance of the characteristic parameters through grey relevance analysis, and the method comprises the following specific steps:
1) the comparison object (evaluation object) and the reference number series (evaluation criterion) are determined. Let m evaluation objects, n evaluation indexes, and x reference number0＝{x0(k) 1,2, …, n, the comparison column being xi＝{xi(k) |k＝1,2,…,n},i＝1,2,…,m。
2) And determining the weight corresponding to each index value. The weight w ═ w corresponding to each index can be determined by an analytic hierarchy process or the like1,…,wn]Wherein w isk(k is 1,2, …, n) is a weight corresponding to the k-th evaluation index.
3) Calculating a gray correlation coefficient formula:
Figure RE-GDA0002960127580000091
for comparison of the correlation coefficient of the sequence xi to the reference sequence x0 on the k-th index, where ρ ∈ [0,1]]Is the resolution factor. Wherein, it is called
Figure RE-GDA0002960127580000092
Two-stage minimum differences and two-stage maximum differences are respectively provided.
Generally, the larger the resolution coefficient ρ, the larger the resolution; the smaller ρ, the smaller the resolution.
4) The gray-weighted relevance is calculated. The grey-weighted relevance is calculated by the formula:
Figure RE-GDA0002960127580000093
in the formula: r isiThe gray-weighted relevance of the i-th evaluation object to the ideal object.
5) And (5) evaluating and analyzing. And sequencing the evaluation objects according to the gray weighted association degree, and establishing the association sequence of the evaluation objects, wherein the greater the association degree is, the better the evaluation result is.
In order to improve the prediction accuracy of the algorithm model, remove some redundant features and facilitate the discovery and the mining of internal features by the GRNN model, the influence factors with small relevance need to be eliminated, and the characteristic factors with large influence on the relevance are selected.
Taking the thickness of the ice coated by the stay cable as output Y(n)，Y(n)＝{Y(1),Y(2),…Y(n)Is given as [ X ] with the factor sequence as the input vectorij]In this document, j groups of data are selected from 5 influencing factors (i ═ 5), and an i × j input matrix is constructed:
Figure RE-GDA0002960127580000101
in the second step, to eliminate the dimension effect of the variable, normalization (interval value is [0, 1]) is used to preprocess the data, and the basic formula is:
Figure RE-GDA0002960127580000102
wherein x isminIs the minimum value of the original data; x is the number ofmaxIs the maximum of the original data.
In the third step, the normalized samples are divided into two groups, each subset data is respectively subjected to a primary verification set, the other subset data is used as a training set, and 2-fold grouping cross verification is obtained, wherein the process is as follows:
the normalized data is processedThe set is randomly equally divided into K sub-data sets { S1,S2,…SkThe specific method of the invention is as follows: each subset SiAnd respectively making a verification set once, and taking the rest K-1 sub-data sets as training sets to obtain predicted values under K (an example when K is 2 is given in the specification) models.
Transferring the grouped training sample set (input variable) to a mode layer, wherein the neuron number of the mode layer is equal to the number j of the learning samples, and the transfer function of the mode layer is as follows:
Figure RE-GDA0002960127580000103
x in the formula is a network input variable; xiThe learning sample corresponding to the ith neuron.
Two types of neurons are used in the summation layer for summation. One of them is to sum the outputs of all the neurons in the mode layer, where the connection weight between the mode layer and each neuron is 1, and the transfer function is:
Figure RE-GDA0002960127580000104
the other type performs weighted summation on neurons of all mode layers, and the transfer function is:
Figure RE-GDA0002960127580000105
wherein the connection weight of the ith neuron in the mode layer and the jth numerator summation neuron in the summation layer is the ith output sample YiThe jth element in (a);
the number of neurons in the output layer is equal to the dimension k of the output vector in the learning sample, the output of each neuron summation layer is divided, and the output of the neuron j corresponds to the estimation result
Figure RE-GDA0002960127580000111
J (d) ofThe elements, namely:
Figure RE-GDA0002960127580000112
in the fourth step, the Mean Square Error (MSE) of the output value of the training sample and the actual value is used as a fitness function; in the determined search space, each individual self optimal solution is searched through iteration, in each iteration, the individual can search an extreme value pbest and a global extreme value gbest, and the self position is updated mainly through a formula, wherein the updating formula is as follows:
Figure RE-GDA0002960127580000113
wherein: t is the number of iterations; xtIs the current position vector;
Figure RE-GDA0002960127580000114
the current global optimal position vector is obtained;
Figure RE-GDA0002960127580000115
to enclose the step size, coefficient vectors a and C are defined as follows:
A＝2a*rand1-a (9)
C＝2*rand2 (10)
wherein, rand1And rand2Is [0,1]]Random numbers generated uniformly within the range; a is a convergence factor, which decreases linearly from 2 to 0 with the number of iterations t, i.e.:
a＝2-2t/tmax (11)
tmaxis the maximum number of iterations.
With the reduction of the convergence factor a, the individual position can reach the optimal position between the time t and the global position at the time t +1, which means that the individual position always moves in the contraction enclosure in the optimization process, and in order to achieve the effect of the optimization mode, the individual position is searched in a spiral motion mode, and the mathematical model is as follows:
Figure RE-GDA0002960127580000116
wherein:
Figure RE-GDA0002960127580000117
as the distance between whale and the current globally optimal individual, b is a limiting constant, and l is [ -1,1 [ -1]A random number in between.
In order to solve the synchronization problem of whale individuals in hunting behaviors, the selected contraction surrounding mechanism and the spiral updating position probability are both assumed to be 0.5, and the model is as follows:
Figure RE-GDA0002960127580000121
wherein P is a random number generated uniformly distributed within [0,1 ].
When the coefficient vector | A | >1 represents that whales swim outside the contraction enclosure, the whale individuals randomly search according to the positions of the whales, and the mathematical model is as follows:
Figure RE-GDA0002960127580000122
wherein,
Figure RE-GDA0002960127580000123
is a randomly selected whale individual position vector.
Given cross probability PcFor the corresponding individual WiAnd WjIs crossed, wherein the cross formula is as follows:
Figure RE-GDA0002960127580000124
wherein the formula is as follows: alpha is alpha1And alpha2Is [0,1]]A random number in between;
given probability of variation PmAnd carrying out mutation operation on the individuals to obtain new individuals.
Figure RE-GDA0002960127580000125
f(g)＝r2(1-g/Gmax) (17)
In the formula amaxAnd aminIs represented as gene aijUpper and lower bounds of (1); r is2Is usually [0,1]]The random number of (1); wherein g represents the current iteration number; gmaxThe maximum number of evolutions;
and updating the local extremum and the global extremum. And comparing the current fitness value with the historical optimal fitness value, if the current fitness value is more optimal, updating the current fitness value to be a local extremum pbest, further comparing the current fitness value with the global extremum, and selecting the optimal value as the global extremum gbest.
If p <0.5 and | A | > is more than or equal to 1, the invention uses the particle swarm optimization for reference, and the output value is subjected to self-adaptive variation updating, and the formula is as follows:
Figure RE-GDA0002960127580000126
Figure RE-GDA0002960127580000127
in the formula, ω is a weight coefficient, GmaxTo the maximum number of iterations, GiFor the current number of iterations,
Figure RE-GDA0002960127580000128
for the current global optimal position vector, a and C are both coefficient vectors.
And judging whether a termination condition is reached. The maximum iteration number is selected as a termination condition, and if the maximum iteration number is reached, the calculation is stopped. If not, jumping to step four. The fitness value is recalculated. And (5) calculating the individual fitness value after genetic manipulation.
And selecting an individual position corresponding to the minimum fitness value, namely a smoothing factor sigma, establishing a GRNN model by using the optimal smoothing factor, and predicting the test sample.
In order to solve the problems that the genetic algorithm is complex in structure and the whale algorithm is easy to fall into local optimum, the invention also comprises a method for acquiring the individual fitness value, which comprises the following steps,
step 1) searching a local extreme value pbest;
step 2) searching a global extreme value gbest;
step 3), updating the local extreme value and the global extreme value;
and 4) judging whether a termination condition is reached, if so, stopping, otherwise, jumping to the step 1), and searching for the fitness value again.
And taking the mean square error of the output value and the actual value of the training sample as a fitness function, searching the self optimal solution of each individual through iteration in a determined search space, and searching a local extremum pbest and further searching a global extremum gbest in each iteration.
When searching for the local extremum pbest and the global extremum gbest, the self position is continuously updated, and the searching is performed in a spiral motion mode.
In step 3), when updating the local extremum and the global extremum, comparing the current fitness value with the historical optimal fitness value, if the current fitness value is better than the historical optimal fitness value, updating the current fitness value to the local extremum pbest, further comparing the current fitness value with the global extremum, and selecting the optimal value as the global extremum gbest.
The method introduces the crossover and mutation operators of the GA algorithm into the WOA algorithm, updates and optimizes individual population, avoids the WOA algorithm from falling into local optimal solution, has simple structure, is used for short-term icing thickness prediction, establishes a GRNN model, and greatly improves the operation speed and the actual processing efficiency when a test sample is predicted.
Example (b):
set the thickness of the ice coating as a reference sequence to x0(p) using n (n ═ 35) sets of data: x is the number of0(p)＝{x0(1),x0(2),…,x0(n) }; the inclination angle, diameter, ambient temperature, relative humidity, ambient wind speed, precipitation and air pressure of the stay cable are used as comparison sequencesColumn, set to xi(t) wherein there are m (m ═ 5) subsequences, each subsequence corresponding to n data: x is the number ofi(p)＝{xi(1),xi(2),…,xi(n)}。
And substituting the preprocessed reference sequence and the comparison sequence into a grey correlation analysis formula to calculate the comprehensive correlation degree between the icing and the related parameters. And (3) obtaining grey correlation results between various correlation factors and the icing thickness by using MATLAB programming calculation:
TABLE 1 Grey correlation analysis of various influencing factors with icing thickness
Figure RE-GDA0002960127580000141
In the example, influence factors with the relevance smaller than 0.5 are removed, five characteristic values with high relevance are reserved, the data set comprises temperature, rainfall, wind speed, relative humidity and icing thickness under 5 dip angles, and the sample continuity is good. In the example of the neural network training, the environmental temperature, the relative humidity, the wind speed, the rainfall and the icing thicknesses at different inclination angles between 18:00 and 11:00 of the next day in the test record are selected, the time interval of data acquisition is 30min, 35 groups of sample data are totally obtained, and the data table 2 shows that:
TABLE 2 sample data
Figure RE-GDA0002960127580000142
Figure RE-GDA0002960127580000151
Further, the sample data is divided into training samples and test samples, wherein numbers 1-25 are used as training samples, and numbers 26-35 are used as model test samples. Selecting an inclination angle (i is equal to 1), a temperature (i is equal to 2), humidity (i is equal to 3), wind speed (i is equal to 4) and rainfall (i is equal to 5) as input vectors [ Xij]Using the thickness of the ice coating as output data Y(n)，n＝25，Constructing a training sample matrix;
according to a normalization formula, performing normalization processing on the training samples; dividing the test samples into two groups for cross validation; inputting the training sample into the GRNN network; in the GRNN network, a regression problem between independent variables and non-independent variables is solved, and the probability density f (x, y) is assumed to be combined by random variables x and y, wherein x is x0Then y for x0The regression value of (d) may be expressed as:
Figure RE-GDA0002960127580000161
according to Parzen non-parametric estimation, the probability density function f (x)0Y) can be expressed as:
Figure RE-GDA0002960127580000162
Figure RE-GDA0002960127580000163
d(y,yi)＝(y-yi)2 (23)
where n is the capacity of the training sample, p is the dimension of the random variable x, and σ is the smoothing factor.
Generating individual population scale of the smoothing factor, setting related parameters of a GA algorithm and a WOA algorithm, such as parameters of iteration times, population scale, individual dimension, variation probability, cross probability and the like, and randomly initializing algorithm parameters;
each individual fitness value is calculated. The Mean Square Error (MSE) formula of the output value and the actual value of the training sample is selected as a fitness function, and is as follows:
Figure RE-GDA0002960127580000164
wherein the output values in the training samples are:
Figure RE-GDA0002960127580000165
actual values in the sample data: y ═ y1,y2,…,yn}
Calculating the fitness value of each whale individual by taking the mean square error of an output value and an actual value in a GRNN network training sample as a fitness function, and finding out a global optimal value;
entering the algorithm main loop, judging that p is less than 0.5 and | A | is less than 1, updating the current position formula as (25)
X(j+1)＝X(j)-A*D (26)
Further selecting the global optimal individual and the current individual to carry out the operation of the genetic algorithm according to the set cross probability PcAnd performing cross operation on the individual positions, wherein the cross formula is as follows:
Figure RE-GDA0002960127580000171
if p is less than 0.5 and | A | ≧ 1, updating the individual position according to (23);
X(j+1)＝Xrand-A*D (28)
if P ≧ 0.5, the individual follows the formula with variation probability PmCarrying out variation operation on the individual to obtain a new population, wherein the variation operation formula is as follows:
Figure RE-GDA0002960127580000172
f(g)＝r2(1-g/Gmax) (30)
if p <0.5 and | A | > is more than or equal to 1, carrying out adaptive variation updating on the output value, wherein the formula is as follows:
Figure RE-GDA0002960127580000173
Figure RE-GDA0002960127580000174
where ω is a weight coefficient, Gmax is the maximum number of iterations, Gi is the current number of iterations,
Figure RE-GDA0002960127580000175
for the current global optimal position vector, a and C are both coefficient vectors.
And updating the local extremum and the global extremum. And comparing the current fitness value with the historical optimal fitness value, if the current fitness value is more optimal, updating the current fitness value to be a local extremum pbest, further comparing the current fitness value with the global extremum, and selecting the optimal value as the global extremum gbest.
And judging whether a termination condition is reached. The maximum iteration number is selected as a termination condition, and if the maximum iteration number is reached, the calculation is stopped. Otherwise, the step of updating the individual position is further skipped.
And selecting an individual position vector value corresponding to the minimum fitness value, namely a smoothing factor sigma, establishing a GRNN model by using the optimal smoothing factor, and predicting the test sample.
As shown in fig. 3 and table 2, the difference between the predicted value curve and the actual value of the model of the GRNN network and the WOA-GRNN neural network is large, and although the GA-PSO-optimized GRNN network is improved to some extent compared with the former two, the PSO algorithm is weak in global search capability, so that the predicted values and the actual values of the last 5 groups have large deviations. As can be seen from the curve of the predicted value in FIG. 3, after the complementation of the genetic algorithm and the whale algorithm, the fitting effect of the GA-WOA-GRNN prediction model is better, the prediction performance is superior to that of other 3 models, the trend of ice coating development is basically matched, and the predicted value is closer to the actual value.
Four-model prediction effect evaluation table
Tab.3 Evaluation table of prediction effect of 4 models
Figure RE-GDA0002960127580000181
The relative error of the GA-WOA-GRNN stay cable icing prediction model provided by the method is below 4%. Compared with a GRNN network prediction model, a WOA-GRNN network prediction model and a GA-PSO-GRNN network prediction model, the average relative error of the prediction model provided by the invention is respectively reduced by 63.8%, 47.6% and 37% compared with that of the former 3; compared with a PSO-GRNN prediction model, the root mean square error of the GRNN prediction model after GA-WOA optimization is reduced to 0.58. Therefore, the GA-WOA-GRNN prediction model provided by the method can further reduce prediction errors and improve prediction accuracy.

Claims (10)

1. A method for predicting the short-term icing thickness of a stay cable based on a GA-WOA-GRNN network is characterized by comprising the following steps of:
the method comprises the following steps: according to the growth rule of the icing of the stay cable, selecting the influence factors with larger cable icing relevance, and determining a training set and a test set of sample data;
step two: carrying out data normalization processing on the sample data;
step three: dividing the normalized data into a plurality of groups by using a cross validation method, wherein each group of data is used as an input sample of a GRNN prediction model, and a corresponding icing thickness value is used as an output value of the model to construct a GRNN model training sample matrix;
step four: optimizing a smoothing factor sigma of a GRNN (generalized regression neural network) algorithm by using a GA-WOA (genetic algorithm-word on array) optimization algorithm, taking the mean square error of an output value and an actual value of a training sample as a fitness function, and obtaining a minimum error prediction model in a prospective manner, wherein the model is a finally trained model;
step five: optimizing a smoothing factor of the GRNN, and inputting influence factor data obtained by latest actual measurement and corresponding icing thickness data serving as test samples into a finally trained model for prediction;
and predicting the short-term icing thickness of the stay cable through the steps.
2. The method as claimed in claim 1, wherein the method comprises continuously optimizing a smoothing factor of the GRNN network by determining whether the predetermined maximum number of iterations is reached.
3. The method for predicting the short-term icing thickness of the stayed cable based on the GA-WOA-GRNN network as claimed in claim 1, wherein in the first step, the selection of the influence factors with greater cable icing relevance comprises the selection of meteorological information of the stayed cable and parameter information of the stayed cable, and near-day short-term data information is selected during the selection, wherein the meteorological information data of the stayed cable comprise temperature, relative humidity, precipitation, wind speed, air pressure and the like; the parameter information of the stay cable mainly comprises the inclination angle and the diameter of the stay cable, and the correlation degree of the characteristic parameter information is obtained by adopting grey correlation analysis.
4. The method for predicting the short-term icing thickness of the stay cable based on the GA-WOA-GRNN network as claimed in claim 3, wherein when selecting the influence factor with larger cable icing relevance, the correlation degree of a plurality of characteristic parameter information obtained by grey correlation analysis is specifically adopted by the following steps:
1) determining a comparison object (evaluation object) and a reference number sequence (evaluation standard), wherein m evaluation objects are provided, n evaluation indexes are provided, and x is the reference number sequence0＝{x0(k) 1,2, …, n, the comparison column being xi＝{xi(k)|k＝1,2,…,n},i＝1,2,…,m；
2) The weight corresponding to each index value is determined, and the weight w corresponding to each index can be determined by an analytic hierarchy process or the like [ w [ [ w ]1,…,wn]Wherein w isk(k is 1,2, …, n) is a weight corresponding to the kth evaluation index;
3) calculating a gray correlation coefficient formula:
Figure FDA0002861580770000021
for comparison of the correlation coefficient of the sequence xi to the reference sequence x0 on the k-th index, where ρ ∈ [0,1]]To distinguish the coefficients, among others
Figure FDA0002861580770000022
Respectively a two-stage minimum difference and a two-stage maximum difference;
4) calculating the gray weighted association degree, wherein the calculation formula of the gray weighted association degree is as follows:
Figure FDA0002861580770000023
in the formula: r isiGray weighted relevance of the ith evaluation object to the ideal object; w is aiThe weight corresponding to the ith evaluation index;
5) and evaluation analysis, namely sequencing all the evaluation objects according to the gray weighted association degree, and establishing the association sequence of the evaluation objects.
5. The method for predicting the short-term ice coating thickness of a guy cable based on GA-WOA-GRNN network as claimed in one of claims 1 to 4, wherein in step one,
taking the thickness of the ice coated by the stay cable as output Y(n)，Y(n)＝{Y(1),Y(2),…Y(n)Is given as [ X ] with the factor sequence as the input vectorij]Constructing an input matrix of i × j:
Figure FDA0002861580770000024
6. the method for predicting the short-term icing thickness of the stay cable based on the GA-WOA-GRNN network as claimed in claim 1, wherein in the third step, the normalized samples are grouped, each subset data is respectively subjected to a primary verification set, and the other subset data is used as a training set to obtain multi-fold grouped cross-validation, specifically comprising the following steps:
the normalized data set is randomly divided equally into K sub-data sets { S1,S2,…SkEvery subset SiMake a verification set and the restK-1 sub-data sets are used as training sets to obtain predicted values under K models;
transferring the grouped training sample set (input variable) to a mode layer, wherein the neuron number of the mode layer is equal to the number j of the learning samples, and the transfer function of the mode layer is as follows:
Figure FDA0002861580770000031
x in the formula is a network input variable; xiLearning samples corresponding to the ith neuron;
and in the summation layer, two types of neurons are used for summation, wherein one type is that the output of all the neurons of the mode layer is arithmetically summed, the connection weight value of the mode layer and each neuron is 1, and the transfer function is as follows:
Figure FDA0002861580770000032
the other type performs weighted summation on neurons of all mode layers, and the transfer function is:
Figure FDA0002861580770000033
wherein the connection weight of the ith neuron in the mode layer and the jth numerator summation neuron in the summation layer is the ith output sample YiThe jth element in (a);
the number of neurons in the output layer is equal to the dimension k of the output vector in the learning sample, the output of each neuron summation layer is divided, and the output of the neuron j corresponds to the estimation result
Figure FDA0002861580770000034
The jth element of (a), namely:
Figure FDA0002861580770000035
7. a method for predicting the short-term ice coating thickness of a stayed cable based on GA-WOA-GRNN network as claimed in claim 1,2, 3, 4 or 6, wherein in step four, the Mean Square Error (MSE) of the output value and the actual value of the training sample is used as the fitness function; in the determined search space, each individual self optimal solution is searched through iteration, in each iteration, the individual can search an extreme value pbest and a global extreme value gbest, and the self position is updated, wherein the updating formula is as follows:
Figure FDA0002861580770000036
wherein: t is the number of iterations, XtIs the current position vector;
Figure FDA0002861580770000037
the current global optimal position vector is obtained;
Figure FDA0002861580770000038
to enclose the step size, coefficient vectors a and C are defined as follows:
A＝2a*rand1-a (8)
C＝2*rand2 (9)
the coefficient vectors A and C are obtained from equations (8) and (9), where rand1And rand2Is [0,1]]A generated random number; a is a convergence factor, which decreases linearly from 2 to 0 with the number of iterations t, i.e.:
a＝2-2t/tmax (10)
wherein, tmaxIs the maximum iteration number;
with the reduction of the convergence factor a, the individual position can reach the optimal position between the time t and the global position at the time t +1, which means that the individual position always moves in the contraction enclosure in the optimization process, and in order to achieve the effect of the optimization mode, the individual position is searched in a spiral motion mode, and the mathematical model is as follows:
Figure FDA0002861580770000041
wherein:
Figure FDA0002861580770000042
as the distance between whale and the current globally optimal individual, b is a limiting constant, and l is [ -1,1 [ -1]Random numbers generated uniformly in between;
in order to solve the synchronization problem of whale individuals in hunting behaviors, the selected contraction surrounding mechanism and the spiral updating position probability are both assumed to be 0.5, and the model is as follows:
Figure FDA0002861580770000043
wherein P is random numbers generated in [0,1] in uniform distribution;
when the coefficient vector | A | >1 represents that whales swim outside the contraction enclosure, the whale individuals randomly search according to the positions of the whales, and the mathematical model is as follows:
Figure FDA0002861580770000044
wherein,
Figure FDA0002861580770000045
a randomly selected whale individual position vector;
given cross probability PcFor the corresponding individual WiAnd WjThe position of (a) is crossed, and the cross formula is as follows:
Figure FDA0002861580770000046
wherein the formula is as follows: alpha is alpha1And alpha2Is a group of a value of [0,1]a random number in between;
given probability of variation PmCarrying out mutation operation on individuals to obtain new individuals;
Figure FDA0002861580770000047
f(g)＝r2(1-g/Gmax) (16)
in the formula amaxAnd aminIs represented as gene aijUpper and lower bounds of (1); r is2Is usually [0,1]]The random number of (1); g represents the current iteration number; gmaxThe maximum number of evolutions;
if p <0.5 and | A | > is more than or equal to 1, the invention uses the particle swarm algorithm for reference to adaptively vary and update the output value, and the formula is as follows:
Figure FDA0002861580770000051
Figure FDA0002861580770000052
omega is a weight coefficient, GmaxTo the maximum number of iterations, GiFor the current number of iterations,
Figure FDA0002861580770000053
for the current global optimal position vector, A and C are both coefficient vectors;
updating a local extreme value and a global extreme value, comparing the current fitness value with the historical optimal fitness value, if the current fitness value is better than the historical optimal fitness value, updating the current fitness value to be a local extreme value pbest, further comparing the current fitness value with the global extreme value, and selecting an optimal value as a global extreme value gbest;
judging whether a termination condition is reached, selecting the maximum iteration number as the termination condition, and stopping calculation if the maximum iteration number is reached; if not, jumping to the step four; recalculating the fitness value; updating the global extreme value gbest again;
and selecting an individual position corresponding to the minimum fitness value, namely a smoothing factor sigma, establishing a GRNN model by using the optimal smoothing factor, and predicting the test sample.
8. A method for obtaining a fitness value of an individual, comprising the steps of,
step 1) searching a local extreme value pbest;
step 2) searching a global extreme value gbest;
step 3), updating the local extreme value and the global extreme value;
step 4) judging whether a termination condition is reached, if so, stopping, otherwise, jumping to the step 1), and searching for the fitness value again;
and taking the mean square error of the output value and the actual value of the training sample as a fitness function, searching the self optimal solution of each individual through iteration in a determined search space, and searching a local extremum pbest and further searching a global extremum gbest in each iteration.
9. The method of claim 8, wherein the local extremum pbest and the global extremum gbest are searched, the self position is continuously updated, and the search is performed in a spiral motion.
10. The method of claim 8 or 9, wherein in step 3), when updating the local extremum and the global extremum, the current fitness value is compared with the historical optimal fitness value, if the current fitness value is better than the historical optimal fitness value, the current fitness value is updated to the local extremum pbest, and the optimal value is further compared with the global extremum to be used as the global extremum gbest.
CN202011568052.0A 2020-12-25 2020-12-25 Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network Pending CN112861418A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011568052.0A CN112861418A (en) 2020-12-25 2020-12-25 Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011568052.0A CN112861418A (en) 2020-12-25 2020-12-25 Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network

Publications (1)

Publication Number Publication Date
CN112861418A true CN112861418A (en) 2021-05-28

Family

ID=75997251

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011568052.0A Pending CN112861418A (en) 2020-12-25 2020-12-25 Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network

Country Status (1)

Country Link
CN (1) CN112861418A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116861694A (en) * 2023-07-24 2023-10-10 四川威鹏电缆制造股份有限公司 Cable temperature prediction method based on artificial intelligence
CN117709204A (en) * 2024-02-05 2024-03-15 国网湖北省电力有限公司经济技术研究院 Method, system and equipment for evaluating stability of pole tower in extreme environment

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106991212A (en) * 2017-03-07 2017-07-28 西安交通大学 A kind of blade root Strength Safety characteristic prediction method for optimizing GRNN network algorithms based on GA_PSO
CN109214449A (en) * 2018-08-28 2019-01-15 华北电力大学 A kind of electric grid investment needing forecasting method
CN109886589A (en) * 2019-02-28 2019-06-14 长安大学 A method of low-carbon Job-Shop is solved based on whale optimization algorithm is improved
CN110895772A (en) * 2019-11-11 2020-03-20 国网浙江省电力有限公司宁波供电公司 Electricity sales amount prediction method based on combination of grey correlation analysis and SA-PSO-Elman algorithm
CN112069911A (en) * 2020-08-11 2020-12-11 安徽理工大学 Fruit and vegetable quality detection method based on multispectral image information and TLMD-WOA-SIFT

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106991212A (en) * 2017-03-07 2017-07-28 西安交通大学 A kind of blade root Strength Safety characteristic prediction method for optimizing GRNN network algorithms based on GA_PSO
CN109214449A (en) * 2018-08-28 2019-01-15 华北电力大学 A kind of electric grid investment needing forecasting method
CN109886589A (en) * 2019-02-28 2019-06-14 长安大学 A method of low-carbon Job-Shop is solved based on whale optimization algorithm is improved
CN110895772A (en) * 2019-11-11 2020-03-20 国网浙江省电力有限公司宁波供电公司 Electricity sales amount prediction method based on combination of grey correlation analysis and SA-PSO-Elman algorithm
CN112069911A (en) * 2020-08-11 2020-12-11 安徽理工大学 Fruit and vegetable quality detection method based on multispectral image information and TLMD-WOA-SIFT

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
何海琳等: "基于改进鲸鱼优化算法的外骨骼机器人步态检测", 《计算机应用》 *
温廷新等: "基于灰色关联熵的煤与瓦斯突出概率神经网络预测模型", 《计算机应用研究》 *
王少熙等, 西北工业大学出版社 *
郑振华: "输电线路覆冰厚度智能识别软件开发", 《中国优秀硕士学位论文全文数据库》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116861694A (en) * 2023-07-24 2023-10-10 四川威鹏电缆制造股份有限公司 Cable temperature prediction method based on artificial intelligence
CN117709204A (en) * 2024-02-05 2024-03-15 国网湖北省电力有限公司经济技术研究院 Method, system and equipment for evaluating stability of pole tower in extreme environment
CN117709204B (en) * 2024-02-05 2024-05-07 国网湖北省电力有限公司经济技术研究院 Method, system and equipment for evaluating stability of pole tower in extreme environment

Similar Documents

Publication Publication Date Title
CN108564192B (en) Short-term photovoltaic power prediction method based on meteorological factor weight similarity day
CN109063911B (en) Load aggregation grouping prediction method based on gated cycle unit network
CN112288164B (en) Wind power combined prediction method considering spatial correlation and correcting numerical weather forecast
CN112116144B (en) Regional power distribution network short-term load prediction method
CN113705877B (en) Real-time moon runoff forecasting method based on deep learning model
CN106251001A (en) A kind of based on the photovoltaic power Forecasting Methodology improving fuzzy clustering algorithm
CN112149879A (en) New energy medium-and-long-term electric quantity prediction method considering macroscopic volatility classification
CN115374995A (en) Distributed photovoltaic and small wind power station power prediction method
CN109143408B (en) Dynamic region combined short-time rainfall forecasting method based on MLP
CN115081592B (en) Highway low-visibility prediction method based on genetic algorithm and feedforward neural network
CN112330027B (en) Search engine index-based power load prediction method
CN114595873B (en) Gray correlation-based DA-LSTM short-term power load prediction method
CN110674965A (en) Multi-time step wind power prediction method based on dynamic feature selection
CN112861418A (en) Short-term icing thickness prediction method for stay cable based on GA-WOA-GRNN network
CN114444378A (en) Short-term power prediction method for regional wind power cluster
CN106600041A (en) Restricted Boltzmann machine-based photovoltaic power generation short-term power probability prediction method
CN111310990A (en) Improved gray combination model-based track quality prediction method and system
CN108832663A (en) The prediction technique and equipment of the generated output of micro-capacitance sensor photovoltaic generating system
CN115994604A (en) Short-term icing thickness prediction method for overhead line power transmission line based on GWO-GA optimization network
CN112766548A (en) Order completion time prediction method based on GASA-BP neural network
CN115018200A (en) Power load prediction method and system based on deep learning and considering multiple influence factors
CN115948964A (en) Road flatness prediction method based on GA-BP neural network
CN118395257A (en) Extra-high voltage transmission line abnormal line loss analysis method for multidimensional microclimate
CN118017482A (en) Flexible climbing capacity demand analysis method based on prediction error feature extraction
CN116960962A (en) Mid-long term area load prediction method for cross-area data fusion

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20210528